This article presents a novel analytical approach to estimate the background component of diffuse irradiance on horizontal surfaces under partially obstructed anisotropic sky, when neighbor orthogonal vertical and horizontal surfaces hide parts of the sky dome. This helps to calculate the incident diffuse radiation onto horizontal roofs of orthogonal buildings using the defined here horizontal anisotropic sky view factors. The case of infinitely long urban canyon also is studied. The resulting equations include an isotropic part and an anisotropic correction. At last the article describes diffuse energy balance principles as a part of the base of anisotropic factor algebra. The article includes examples that demonstrate how new anisotropic view factors can be computed from a set of known factors with the help of anisotropic factor algebra. (C) 2013 Elsevier Ltd. All rights reserved.